JP6173694B2 - Image processing apparatus, X-ray computed tomography apparatus, and image processing method - Google Patents

Description

Embodiments described herein relate generally to an image processing apparatus, an X-ray computed tomography apparatus, and an image processing method .

  Due to image reconstruction in computed tomography (CT), the sequential algorithm may include total variation (TV) minimization. For example, there are several methods based on the ordered subset simultaneous number reconstruction method (OSSART) and the simultaneous number reconstruction method (SART). TV minimization may be applied to images that are reconstructed using an analytical program such as filtered back projection (FBP) to remove noise.

  Despite efforts in the prior art, some problems remain unresolved and improvements are sought. In the prior art, noise in an image is generally removed very uniformly except for edges. In other words, noise is removed based on total variation (TV) minimization, but if the original image has a non-uniform distribution, the resulting image will be transiently smooth in certain regions. In other regions, it still contains noise. On the other hand, when the prior art is applied to an image having fine edges, the edges may disappear due to smoothing. If the original image has a non-uniform noise distribution that is routine in clinical applications, total variation (TV) minimization according to the prior art improves noise without sacrificing spatial resolution It seems impossible.

  Further, in an image including noise in which the HU value is shifted from 2σ to 3σ from the average value and far from the true value, there are some miscellaneous pixel clusters. When TV minimization is performed, these clusters will remain as black / white dots in the denoised image. This is because (1) the “cluster effect” slows down the noise removal, and (2) the original HU value is far from the true value.

  The objective is to provide a practical solution to implement a total variation (TV) minimization algorithm that avoids excessive compensation in low noise regions and reduces dots in high noise pixel clusters. .

The image noise removal apparatus according to the present embodiment is
a) means for initializing a direction index associated with each pixel of the image, wherein the direction index indicates either an increase or a decrease with respect to a discrete gradient of total variation;
b) means for determining a discrete slope of the total variation for each pixel, wherein the discrete slope indicates the increase or the decrease;
c) if the direction index and the discrete gradient are equal, means for changing the pixel value of each pixel by a predetermined value to reduce the total variation;
d) means for repeatedly executing the means b) to the means c) until a predetermined condition is reached .

FIG. 1 is a diagram showing an embodiment of a multi-slice X-ray CT apparatus or scanner according to the present invention. FIG. 2 is a flowchart showing the steps involved in the preferred process of the total variation successive approximation (TV-IR) according to the present invention. FIG. 3 is a flow chart illustrating the steps involved in the ordered subset simultaneous generation reconstruction (OSSART) used in the preferred process of the total variation successive approximation (TV-IR) according to the present invention. FIG. 4 is a flowchart illustrating the steps involved in the discrete TV minimization method used in the preferred process of the total variation successive approximation (TV-IR) according to the present invention. FIG. 5A shows the case of a single odd pixel processed in the conventional process of minimizing total variation according to the prior art. FIG. 5B is a diagram showing an odd pixel cluster processed in the process of minimizing total variation according to the prior art. FIG. 6 is a diagram illustrating an exemplary pixel case processed by the discrete TV minimization method used in the preferred process of total variation successive approximation (TV-IR) according to the present invention. FIG. 7A shows an example processed by the discrete TV minimization method used in the preferred process of the total variation successive approximation (TV-IR) according to the present invention. FIG. 7B shows an example processed by the discrete TV minimization method used in the preferred process of the total variation successive approximation (TV-IR) according to the present invention. FIG. 7C is a diagram illustrating an example processed by the discrete TV minimization method used in the preferred process of total variation successive approximation (TV-IR) according to the present invention. FIG. 7D shows an example processed by the discrete TV minimization method used in the preferred process of the total variation successive approximation (TV-IR) according to the present invention. FIG. 8A shows an image reconstructed from projection data, in which high-level noise is distributed in a non-uniform manner in the image. FIG. 8B is a diagram showing an image reconstructed using the total variation successive approximation method (TV-IR). FIG. 8C shows an exemplary image reconstructed using the total variation successive approximation method (TV-IR) with unidirectional conditions according to the present invention. FIG. 9A shows a series of pixels traversing the edge and their pixel values in the CT number for the original image, after discrete total variation (DTV) minimization, and after total variation (TV) minimization. It is a graph. FIG. 9B is a plot showing enlarged edge portions of the pixels in the blue rectangular box in FIG. 9A.

  Hereinafter, an embodiment of the present invention will be described with reference to the drawings. Components with the same reference numerals are the same components. Referring to FIG. 1, the configuration of a multi-slice X-ray CT apparatus or scanner according to the present embodiment is shown, which includes a gantry 100 and other devices or units. The gantry 100 is shown as viewed from the front, and further includes an X-ray tube 101, an annular frame 102, and a multi-row or two-dimensional array type X-ray detector 103. The X-ray tube 101 and the X-ray detector 103 are installed on an annular frame 102 that rotates about an axis RA in a diametrical direction that crosses the subject S. The rotation unit 107 rotates the frame 102 at a high speed of about 0.27 seconds / rotation while the subject S moves along the axis RA in the direction toward the back of the drawing or in the direction coming out of the drawing.

  The multi-slice X-ray CT apparatus further includes a high voltage generator 109 that applies a tube voltage to the X-ray tube 101 and generates X-rays in the X-ray tube 101. In some embodiments, the high voltage generator 109 is installed in the frame 102. X-rays are emitted toward the subject S, and the cross-sectional area of the subject S is represented by a circle. The X-ray detector 103 is disposed on the opposite side of the X-ray tube 101 across the subject S, and detects X-rays emitted so as to be transmitted through the subject S.

  Still referring to FIG. 1, the X-ray CT apparatus or scanner further includes other devices that process the detected signal from the X-ray detector 103. A data acquisition circuit or data acquisition system (DAS) 104 converts a signal output from the X-ray detector 103 for each channel into a voltage signal, amplifies it, and further converts it into a digital signal. X-ray detector 103 and DAS 104 are configured to process a predetermined total number of projections (TPPR) per revolution.

  The data described above is sent to the preprocessing device 106 installed in the console outside the gantry 100 via the non-contact data transmitter 105. The preprocessing device 106 performs specific corrections such as sensitivity correction on the raw data. Next, the storage device 112 stores the resulting data. This data is also called projection data in the stage immediately before the reconstruction process. The storage device 112 is connected to the system controller 110 via a data / control bus, but includes a reconstruction device 114, a discrete total variation (TV) minimization device 117, a display device 116, an input device 115, and a scan plan support device. The same applies to 200. The scan plan support apparatus 200 includes a function of creating a scan plan by supporting an image engineer.

  One embodiment of reconstruction device 114 and discrete total variation (TV) minimization device 117 further includes various software and hardware components. According to one aspect of the invention, the reconstruction device 114 of the CT apparatus reconstructs the image while the discrete TV minimizing device 117 effectively minimizes the total variation. In general, the reconstruction device 114 and the discrete TV minimization device 117 in one embodiment of the present invention perform a total variation successive approximation (TVIR) algorithm to reconstruct an image. More particularly, the reconstruction device 114 performs an ordered subset contemporaneous reconstruction (OSSART) process on the projection data while the discrete TV minimization device 117 performs the TV minimization process. One embodiment of the reconstruction device 114 and the discrete TV minimizing device 117 respectively includes a main loop in which a first predetermined number of iterations are defined and an inner loop in which a second predetermined number of iterations are defined. Perform two processes implemented in. In another embodiment, the discrete TV minimizing device 117 repeats the inner loop until a predetermined predetermined condition is achieved.

  Prior to the TV minimization process, reconstruction device 114 performs an ordered subset contemporaneous reconstruction (OSSART) on the projection data. Projection data is grouped into a predetermined number of subsets N, each having a specific number of views. During OSSART, each subset is processed sequentially in one embodiment. In another embodiment, these multiple subsets may be processed in parallel by utilizing a specific microprocessor, such as a plurality of central processing units (CPUs) or graphics processing units (GPUs). . In yet another embodiment, the reconstruction device 114 performs an ordered subset contemporaneous reconstruction (OSSART) on the projection data using the relaxation parameters.

  During the ordered subset contemporaneous reconstruction (OSSART), the reconstruction device 114 further performs two important operations. That is, for each subset N, the reconstruction device 114 re-projects the image volume to form calculated projection data, which is calculated as measured projection data when added to the current image evaluation. Backproject the normalized difference from the projected data to reconstruct the updated image volume. More specifically, in one embodiment of the reconstruction device 114, the image volume is reprojected by using a ray tracing method in which none of the coefficients of the system matrix are cached. Further, in one embodiment of the reconstruction device 114, all rays in a subset are reprojected simultaneously, but this is optional but implemented in parallel. Other embodiments include system models and noise models. In backprojection, one embodiment of the reconstruction device 114 uses a pixel drive method to backproject all of the normalized difference projection data in a subset to obtain the desired updated image volume. Form. Since the reconstruction device 114 backprojects the sum or difference projection data of all rays in a subset to form an image volume, this operation is also optional but implemented in parallel. By applying these operations to all the subsets N, one OSSART step is completed. This embodiment and the other embodiments are optional, but are included in the scope of the present invention described in the claims.

  In the total variation (TV) minimization process, the discrete TV minimization device 117 performs discrete TV minimization using a predetermined step parameter and number of steps to adjust a given pixel value. Although optional, one-way conditions apply. As described below with reference to FIG. 6, a predetermined unidirectional condition reduces noise in high noise regions while avoiding that certain low noise regions are transiently compensated or excessively smoothed. . In discrete TV minimization, if a pixel is on an edge, its pixel value remains exactly the same throughout the noise removal. In other words, in one embodiment of the discrete TV minimization device 117, blur edges in the image are substantially reduced. Furthermore, in one embodiment of the discrete TV minimization device 117, the denoised and unnatural noise texture, especially after strong denoising, is substantially improved. In one embodiment of the discrete TV minimizing device 117, the discrete TV minimization ends when a predetermined condition is reached. An exemplary termination condition is zero slope due to a unidirectional condition, and as another example, discrete TV minimization may be repeated a predetermined number of times.

  In the above-described multi-slice X-ray CT apparatus or scanner according to the present invention, one embodiment of the reconstruction device 114 reconstructs an image based on a successive approximation method. In another embodiment of the reconstruction device 114, the image is reconstructed based on an analytical reconstruction method such as filtered back projection (FBP). Furthermore, the above-described embodiments of the multi-slice X-ray CT apparatus or scanner according to the present invention include separate devices for the reconstruction device 114 and the discrete TV minimization device 117. In other embodiments, reconstruction device 114 and discrete TV minimization device 117 are optional, but are a single device that includes a combination of software and hardware. The present invention is implemented to improve noise texture after denoising based on discrete TV minimization with one-way conditions, without being limited to any specific hardware and software combination. The

  Referring now to FIG. 2, a flow chart shows the steps involved in an exemplary process of total variation successive approximation (TV-IR) according to the present invention. In the initialization step S10, the image X0 is initialized to zero. In the same step, a value indicating the number of iterations is initialized to a first predetermined number K, and the current number of iterations is maintained in the iteration counter or main loop counter k. In step S20, an ordered subset contemporaneous reconstruction (OSSART) using relaxation parameters is performed on the measured projection data in the exemplary TV-IR process according to the present invention. Step S20 outputs an intermediate image X1. Detailed steps of the OSSART will be described later with reference to FIG.

Still referring to FIG. 2, the exemplary process shown includes two loops in which certain steps are repeated and / or performed sequentially. The first loop is a main loop or an outer loop including step S20, step S30, and step S40. The main loop is repeated according to the first predetermined number K assigned to the main loop counter k in step S10 according to this exemplary process. When each iteration of the main loop is completed, the main loop counter k is decremented by 1 from the initial value K. In one exemplary process, the first predetermined number K is optional but is determined based on the number of ordered subsets N _sets of projection data. This will be described later with reference to FIG. In the main loop, an ordered subset contemporaneous reconstruction (OSSART) using the relaxation parameter lambda is applied to the projection data in step S20. The weight value is stored in the relaxation parameter λ for OSSART.

  The second loop is a sub-loop or inner loop including step S30 and step S40. The sub-loop is also called a total variation step (TV step) loop. The sub-loop is repeated according to a second predetermined number S assigned to the total variation counter or sub-loop counter s in one embodiment. Steps S30 and S40 are repeated in the sub-loop in this embodiment by the assigned second number S. When each iteration of the sub-loop ends, the sub-loop counter s is decremented by 1 from the initial value S. In another embodiment, steps S30 and S40 are repeated in a sub-loop until a predetermined condition is reached.

  In step S30, the discrete total variation minimization method is executed sequentially so as to minimize the total variation based on a predetermined technique. When step S30 ends, an image X2 is generated from the intermediate image X1 from step S20. The image generated in step S30 is assigned to the intermediate image holder or variable X1 in step S40.

  In step S42, it is determined whether or not the sub-loop has ended based on the sub-loop counter s or a predetermined end condition. If it is determined in step S42 that the sub-loop has ended, it is further determined in step S44 whether or not steps S20 to S40 should be repeated in the main loop. On the other hand, if it is determined in step S42 that the sub-loop has not yet ended, steps S30 and S40 are repeated in the sub-loop.

  In step S44, it is determined whether or not the main loop has ended based on the main loop counter k. If it is determined in step S44 that the main loop has ended, the image X2 is output in step S50. On the other hand, if it is determined in step S44 that the main loop has not yet ended, step S20, step S30, and step S40 are repeated in the main loop.

Referring now to FIG. 3, a flow chart shows further acts or sub-steps in step S20 of FIG. 2, which are exemplary processes of a total variation successive approximation (TV-IR) according to the present invention. Included in the Ordered Subset Contemporaneous Reconstruction Method (OSSART) using the relaxation parameters used in. The illustrated process of OSSART includes one loop in which certain steps are repeated and executed sequentially. This loop includes step S23, step S24 and step S25, and is repeated according to a predetermined number N _sets rather than satisfying a particular condition. When the loop ends, OSSART outputs the intermediate image to the variable X1 in step S27.

  Further, with reference to FIG. 3, each of step S21 to step S26 will be generally described below. In step S21, the image X0 and the measured projection data p are obtained through step S20 in FIG. In an optional implementation, one of the weight values stored in the first predetermined recording structure is selected based on an index k corresponding to the value of the main loop counter k of the main loop, and relaxed Assigned to the parameter λ.

In step S22, the measured projection data p is divided into N _sets groups called subsets. The number of subsets N _sets is based on a specific rule that the total number of views is divided by a predetermined number of subviews. For example, if the projection data has a total of 1200 views and the predetermined number of subviews is 15, the number of subsets is 80, which is obtained by dividing 1200 by 15. Alternatively, the number of views in each subset is optional but varies. If the total number of views is fixed and the number of subsets is relatively small due to the large number of subviews, image convergence is slow and more iterations are required in the main loop. On the other hand, if the number of subsets is relatively high due to the small number of subviews, the image converges faster and requires fewer iterations. At the same time, the image contains more noise. Based on the relationship described above, the value of the first predetermined number K is optional but is modified in step S10 of FIG.

Each subset N _sets includes a number of sub- _rays N _subrays , and this number is determined by dividing the total number of arrays N _rays by the subset N _sets . For each subset N _sets , step S23 reprojects the image X0 to form calculated projection data. In contrast, step S24 backprojects the normalized difference between the measured projection data and the calculated projection data. More specifically, an exemplary process in step S23 reprojects the image volume by using a ray tracing method in which none of the system matrix coefficients are cached. Furthermore, in one embodiment of step S23, all rays in a subset are reprojected simultaneously, but this is optional but implemented in parallel. In backprojection, one embodiment of step S24 backprojects all of the normalized difference projection data in a subset using a pixel drive method to form the desired updated image volume. To do. Since step S24 backprojects the sum of all rays in a subset forming the image volume, i.e. the normalized difference projection data, this operation is also optional but implemented in parallel. When these operations are applied to all the subsets N _sets , one OSSART step is completed. After being initialized to N _sets , the subset counter is decremented by 1 each time each operation ends.

Still referring to FIG. 3, step S25 updates the image X0 by adding the backprojected and weighted image from step S24 to the image X0. To weight the backprojected image, a relaxation parameter λ is used as will be described later with reference to FIG. As a result, in step S26, it is determined whether N _sets have already been completed. If it is determined in step S26 that N _sets has not yet been completed, the loop is repeated by proceeding to step S23. On the other hand, if it is determined in step S26 that N _sets have already been completed, the image generated in step S25 is assigned to the intermediate image holder or variable X1 before the image X1 is output in step S27. .

  Referring now to FIG. 4, the flow chart shows further steps of step S30 of FIG. 2, which are discrete total variation used in the total variation successive approximation (TV-IR) process according to the present invention. (TV) Includes minimization method. The illustrated process of the discrete TV minimization method includes a sub-loop in which specific steps are repeated and performed sequentially. This sub-loop includes steps S110 to S160 and is repeated a predetermined number of times and / or until a specific condition is met. When the sub-loop ends, the discrete TV minimization method returns the image to the variable X2.

  Further, with reference to FIG. 4, each of steps S100 to S170 will be generally described below. In step S100, the direction index DI is initialized to a predetermined value such as 0 for each pixel. The predetermined value 0 in this case means “mixing of increasing tendency and decreasing tendency (also referred to as unknown)” in the direction change with respect to the total variation for a given pixel. Similarly, a predetermined value of 1 means an increase in directional change for the total variation for a given pixel, while a predetermined value of -1 means a decrease in directional change for the total variation for a given pixel. To do. In step S110, the total variation (TV) gradient GR is determined for a given pixel i and the corresponding value is stored in GR [i]. The sign of the total variation gradient GR indicates an increase by +1, a decrease by -1, or a mixture by 0 for a given pixel i. In step S120, it is determined whether or not the corresponding pixel i is 0, that is, mixed, as the direction index DI [i] is initialized. If it is determined in step S120 that the direction index DI [i] is 0, that is, mixed, the direction index DI [i] is updated to the corresponding code of the gradient GR [i] in step S130. That is, if the gradient GR of the total variation is greater than zero, an increase value +1 is assigned to the direction index DI [i]. Similarly, if the gradient GR of the total variation is less than zero, a decrease value of −1 is assigned to the direction index DI [i]. Finally, if the gradient GR of the total variation is zero, the mixed 0 is assigned to the direction index DI [i]. After step S130, the exemplary process of minimizing discrete total variation proceeds to step S140. On the other hand, if it is determined in step S120 that the direction index DI [i] is 0, that is, not mixed, the direction index DI [i] is not updated in step S130, and an exemplary process for minimizing discrete total variation is The process proceeds to step S140.

  Still referring to FIG. 4, an exemplary process of minimizing the discrete total variation is to determine whether the direction index DI [i] and the gradient GR [i] have the same sign for a given pixel i, step S140. Judge with. If it is determined in step S140 that the direction index DI [i] and the gradient GR [i] have the same sign, in step S150, the pixel value for the given pixel i uses a predetermined constant. Updated. An exemplary value for this predetermined constant is a value obtained by dividing the estimated standard deviation StdD of the original image by N. Here, N is in the range of 10 to 100. After step S150, the exemplary process of minimizing discrete total variation proceeds to step S160. On the other hand, if it is determined in step S140 that the direction index DI [i] and the gradient GR [i] do not have the same sign, the pixel value i is not updated in step S150, and the discrete total variation is not updated. The exemplary process of minimization proceeds to step S160.

  The discrete total variation minimization ends according to a predetermined rule. In step S160, it is determined whether all pixels in the image have been processed. If it is determined that all pixels in the image have not yet been processed, the exemplary process of minimizing discrete total variation returns to step S110 for the remaining unprocessed pixels. On the other hand, if it is determined that all the pixels in the image have already been processed, the exemplary process of minimizing discrete total variation proceeds to step S190, where additional termination conditions are examined in step S190. In an embodiment of the discrete total variation minimization process, the predetermined termination condition is that the direction index DI [i] and the gradient GR [i] have different signs in all pixels, as shown in step S170. That is. If it is determined in step S170 that any of the pixels in the image does not have different signs in the pixel direction index DI [i] and the gradient GR [i], an example of minimizing discrete total variation is illustrated. The process returns to step S110 for additional processing. However, if it is determined in step S170 that all pixels have different signs in the direction index DI [i] and the gradient GR [i], an exemplary process for minimizing the discrete total variation is finish.

  In an alternative embodiment of the discrete total variation minimization process, the termination condition in step S170 is from step S110 to step S110, instead of having different signs in the direction index DI [i] and gradient GR [i] of all pixels. This is achieved by repeating up to S160 a predetermined number of times. If, in step S170, it is determined that the predetermined number of iterations has not yet been achieved, the exemplary process of minimizing discrete total variation returns to step S110 for additional processing. The exemplary predetermined number of iterations N is a value obtained by dividing the estimated standard deviation StdD of the original image by a constant C. Where C is the estimated standard deviation in the image from which noise has been removed. On the other hand, if it is determined in step S170 that a predetermined number of iterations has been achieved, the exemplary process of minimizing discrete total variation ends. The exemplary and alternative embodiments described above do not limit the discrete total variation minimization process according to the present invention.

  FIG. 5A shows the case of a single odd pixel processed in the conventional process of minimizing total variation according to the prior art. In the top diagram, a single pixel b is shown in relation to adjacent pixels a and b, and the value of the single pixel b is much better than its true value in the initial state. It is assumed to be large. After the first update in the discrete total variation minimization, the value of the single pixel b is reduced compared to the original value represented by the dashed line, as shown by the solid line in Update I. Yes. After the second update in the discrete total variation minimization, the value of the single pixel b is either the original value represented by the broken line or the double broken line, as indicated by the solid line in Update II. It is further reduced compared to the first updated value shown.

  FIG. 5B shows the case of a strange pixel cluster processed in the process of minimizing discrete total variation according to the present invention. In the top diagram, pixels 2 and 3 are shown in relation to adjacent pixels 1 and 4, and the values of pixels 2 and 3 are initially much larger than their true values. Assumed. After the first update in the discrete total variation minimization, the value of the single pixel 2 is reduced compared to the original value represented by the dashed line, as shown by the solid line in Update I. Yes. After the second update in Discrete Total Variation Minimization, this time the value of a single pixel 3 is compared with the original value represented by the dashed line, as shown by the solid line in Update II. It is decreasing. As shown in FIGS. 5A and 5B, when a cluster of pixels is adjusted, only one pixel value is updated, so it takes longer to process the cluster. That is, it generally takes more time to cover a miscellaneous cluster than to cover a single pixel.

  FIG. 6 illustrates the case of an exemplary pixel processed by a discrete TV minimization method with a unidirectional condition used in the exemplary process of total variation successive approximation (TV-IR) according to the present invention. In general, the pixel value increases or decreases as determined by the slope at each step. A one-way condition is that each pixel value simply increases or decreases according to a non-zero gradient value determined in the first step. In other words, under the unidirectional condition according to the present invention, the direction change remains the same throughout the discrete total variation minimization and cannot be changed in the middle.

  Still referring to FIG. 6, in the top diagram, a single pixel i is shown in relation to adjacent pixels i−1 and i + 1, and the value of a single pixel i is initially set to It is assumed that it is considerably larger than its true value. That is, pixel i should decrease and the directional index is set to indicate a decrease in the first total variation minimization step. After the first total variation minimization step, the value of a single pixel i has decreased compared to the original value represented by the dashed line, as indicated by the solid line in Update I. After the second total variation minimization step, the value of a single pixel i is represented by the original value represented by the dashed line or the double dashed line, as indicated by the solid line in Update II. There is a further decrease compared to the first updated value. After the third total variation minimization step, because of the one-way condition, the value of a single pixel i is first represented by a double dashed line, as shown by the dashed line in Update III. An increase compared to the updated value is avoided. In other words, after the third update III, the value of a single pixel i is represented by the original value represented by the dashed line or the double dashed line, as indicated by the solid line in update II. Compared to the first updated value, it remains unchanged.

7A-7D illustrate that in one embodiment of the total variation successive approximation (TV-IR) method according to the present invention, the discrete TV minimization technique handles various exemplary cases. In general, a discrete total variation in a one-dimensional discrete distribution is defined by the following formula (1).

The total variation minimization is defined by the following equation (2).

Here, n is 1, 2, 3,..., And a is a constant. The discrete gradient of the total variation is substantially synonymous with the gradient of the discrete total variation and is defined by equations (3) and (4) in this application.

In the one-dimensional case, the value of Equation (4) is either -2, 0, or +2.

Similarly, the gradient direction for the three-dimensional image f (i, j, k) is determined by a function gtv along a predetermined direction as seen in Equation (5).

In the case of two dimensions, since the index k is an image slice index, the value of Equation (5) is any one of −4, −2, 0, +2, and +4. Similarly, the three-dimensional TV gradient for the three-dimensional image f (i, j, k) at a predetermined point is any one of −6, −4, −2, 0, +2, +4, and +6. .

Further, the integer m is determined so as to delete the dot in (i, j, k), where m is defined by the following equation (6).

Here, a is a predetermined value, m is larger than a predetermined threshold value m ₀ , and the point (i, j, k) is an isolated noise dot. An isolated noise dot is deleted by f (i, j, k) = f (i, j, k) + ma / 2gtv (i, j, k). Similarly, the dot value m is determined to delete the dot in (i, j, k), where m is defined by equation (7).

Here, a is a predetermined value, m is larger than a predetermined threshold value m ₀ , and the point (i, j, k) is an isolated noise dot. An isolated noise dot is deleted by f (i, j, k) = f (i, j, k) + ma / 4gtv (i, j, k). Similarly, equations (5) and (7) can be generalized to a predetermined volume for the three-dimensional image f (i, j, k).

Referring now to FIG. 7A, a first signal integrity pattern is shown for an exemplary set of pixel values in a discrete total variation minimization. In the initial state of the pixel values, as shown in the upper diagram of FIG. 7A, the three pixel values increase from the first pixel i-1 to the second pixel i, and from the second pixel i. Increase to the third pixel i + 1. That is, Equation (8) indicates that the pixel value increases while the gradient is zero.

As a result, after the discrete total variation minimization, the updated pixel value at the second pixel i remains the same, as shown in the updated lower diagram of FIG. 7A. With conventional TV minimization, the TV slope value for the pattern of FIG. 7A is typically not zero due to the continuous image model. The pixel value is updated with a non-zero value and the pattern is changed, resulting in edge blurring.

Referring now to FIG. 7B, a second signal integrity pattern is shown for an exemplary set of pixel values in total variation minimization. In the initial state of the pixel value, as shown in the upper diagram of FIG. 7B, the pixel value increases from the first pixel i-1 to the second pixel i, but from the second pixel i to the second pixel i. Decrease to 3 pixel i + 1. That is, Equation (9) indicates that the pixel value increases and then decreases while the gradient is 2 according to Equation (4).

As a result, after the total variation minimization, the value of the second pixel i decreases as shown in the updated lower diagram of FIG. 7B.

Referring now to FIG. 7C, a third signal integrity pattern is shown for an exemplary set of pixel values in total variation minimization. In the initial state of the pixel value, as shown in the upper diagram of FIG. 7C, the three pixel values decrease from the first pixel i-1 to the second pixel i, and from the second pixel i. Decrease to the third pixel i + 1. That is, Equation (10) indicates that the pixel value decreases while the gradient is zero.

Consequently, after the discrete total variation minimization, the updated pixel value at the second pixel i remains the same, as shown in the lower diagram after the update in FIG. 7C.

Referring now to FIG. 7D, a fourth signal integrity pattern is shown for an exemplary set of pixel values in the total variation minimization. In the initial state of the pixel value, as shown in the upper diagram of FIG. 7D, the pixel value decreases from the first pixel i-1 to the second pixel i, but from the second pixel i to the second pixel i. Increase to 3 pixels i + 1. That is, Equation (11) indicates that the pixel value increases after decreasing while the gradient is −2.

As a result, after the discrete total variation minimization, the value of the second pixel i increases as shown in the lower diagram after the update in FIG. 7D.

  FIG. 8A shows an image reconstructed from projection data, which has a high level of noise distributed in the image in a non-uniform manner.

  FIG. 8B shows an image with noise removed from FIG. 8A using discrete total variation minimization. Total variation minimization is used without the one-way condition according to the invention described above. As a result, this image shows that minimizing the total variation has reduced the noise to some extent, but some regions in the image have been compensated transiently after denoising, i.e. Looks like it is over-smoothed. These excessively smoothed regions initially had a relatively low level of noise.

  FIG. 8C shows an exemplary image with noise removed from FIG. 8A using discrete total variation minimization with one-way conditions according to the present invention. Discrete total variation minimization is used with the one-way condition according to the invention described above. As a result, the reconstructed image is substantially reduced in noise by minimizing discrete total variation without transient compensation or excessive smoothing of regions that originally contained relatively low levels of noise. It has been shown.

  Referring now to FIG. 9A, the graph minimizes the discrete total variation (DTV) for a series of pixels crossing an edge, the relationship between their pixel value and CT number, in the case of the original image, by a solid line. The latter case is indicated by a dot-like line, and after the total variation (TV) minimization is indicated by a point-dot-like line. The portion of these pixels that is above the edge is indicated by the blue rectangular box in FIG. 9A. FIG. 9B shows an enlarged edge portion of the pixel in the blue rectangular box of FIG. 9A. The enlarged portion of the pixel value is substantially equal between the original image and after the discrete total variation (DTV) indicated by the dotted line. On the other hand, the enlarged part of the pixel value is slightly different from that after minimizing the total variation indicated by the point dot line.

  As described in the claims, the inventive concept of the present invention does not necessarily include a combination of features including a discrete gradient (DTV) of total variation minimization and a one-way condition for a particular reconstruction algorithm. It is not a requirement. For example, a technique that applies a discrete gradient (DTV) minimization of the total variation without a one-way condition is used with either a predetermined successive approximation algorithm or a predetermined analytical reconstruction algorithm. Similarly, techniques that apply only one-way conditions, without minimizing the total variation discrete slope (RTV), are used with either a predetermined successive approximation algorithm or a predetermined analytical reconstruction algorithm. Furthermore, techniques that apply only one-way conditions are combined with either discrete total variation (DTV) minimization techniques or conventional total variation (TV) minimization techniques. These examples are for illustration only and do not limit the inventive concept of image denoising according to the present invention.

  In general, the features described above have several distinguishable effects on images according to the present invention. For example, the one-way condition improves the noise uniformity in the image after denoising, assuming that the original image has a non-uniform noise distribution, and the excess in the low noise region of the image Avoid smooth smoothing. On the other hand, DTV minimization yields superior results with respect to edge preservation effects when compared to conventional TV minimization. With DTV, the pixel values above the edge are not substantially affected after a certain denoising process. The difference between DTV minimization and conventional TV minimization is substantially negligible for strong edges, while DTV minimization substantially improves the preservation of weak edges. Another distinction is that DTV maintains the original value, but TV smooths the value slightly for pixels near the bottom and top of the edge.

  However, although many features and advantages of the present invention have been described above with details of the structure and function of the present invention, the present disclosure is for illustrative purposes only, particularly with respect to the shape, size, and arrangement of the components. Further, even if changes are made in detail with respect to implementation forms by software, hardware, or a combination of both, those changes are all indicated by the broad and general meaning of the terms used in the claims. It should be understood that the scope is within the scope of the principles of the present invention.

Claims (17)

An image processing apparatus for removing noise in an image,
a) means for initializing a direction index associated with each pixel of the image, wherein the direction index indicates either an increase or a decrease with respect to a discrete gradient of total variation;
b) means for determining a discrete slope of the total variation for each pixel, wherein the discrete slope indicates the increase or the decrease ;
c) if the direction index and the discrete gradient are equal, means for changing the pixel value of each pixel by a predetermined value to reduce the total variation;
d) means for repeatedly executing the means b) to the means c) until a predetermined condition is reached.   The image processing apparatus according to claim 1, wherein the predetermined condition is that the direction index and the discrete gradient are different in a gradient direction for each of the pixels. The image processing apparatus according to claim 1, wherein the predetermined condition is that the means b) to the means c 1 ) are repeatedly executed a predetermined number of times. The gradient direction for the two-dimensional image f (i, j, k) in a predetermined direction is determined by the function gtv:
The image processing apparatus according to claim 1. The Dots value m is determined to remove the dots in the (i, j, k), the dot value m is a as said predetermined value is defined by the following equation,
The image processing apparatus according to claim 1 . Orphaned noise dots, f (i, j, k ) = f (i, j, k) + (ma / 2) gtv (i, j, k) are deleted, the image processing according to claim 5, wherein apparatus. The Dots value m is determined to remove the dots in the (i, j, k), the dot value m is a as said predetermined value is defined by the following equation,
The image processing apparatus according to claim 1 . The image processing apparatus according to claim 5 , wherein when the dot value m is larger than a predetermined threshold value m ₀ , the point f (i, j, k) is an isolated noise dot. The image processing according to claim 8, wherein the isolated noise dot is deleted by f (i, j, k) = f (i, j, k) + (ma / 4) gtv (i, j, k). apparatus. The image processing apparatus according to claim 1, wherein the means a) to the means d 1 ) are executed by a successive approximation method. The image processing apparatus according to claim 1, wherein the means a) to the means d 1 ) are executed by an analytical reconstruction method. e ) means for obtaining image data from the measured data;
f ) means for projecting the image data forward using at least a single ray to generate reprojected data;
g ) means for determining a difference between the reprojected data and the measured data;
h ) means for updating the image data based on the difference and generating an updated image, wherein the means e ) to the means h ) are executed before the means a). Means for generating
i ) means for using the updated image as the image data in the means f ) and the means a) to the means d ), and repeatedly executing the means f ) to the means h ). The image processing apparatus according to claim 1, further comprising: e ) means for obtaining image data from the measured data;
f ) means for projecting the image data forward using at least a single ray to generate reprojected data;
g ) means for determining a data difference between the reprojected data and the measured data;
h ) means for backprojecting said data difference to generate a difference image;
i ) means for performing said means a) to said means d ) on said difference image;
j ) means for updating the image data based on the difference image and generating an updated image, wherein the means e ) to the means i ) are executed before the means a), Means for generating an image;
k ) using the updated image as the image data in the means f ) and the means a) to the means d ), and repeatedly executing the means f ) to the means i ). The image processing apparatus according to claim 1, further comprising: An X-ray computed tomography apparatus for removing image noise,
A reconstruction device for reconstructing an image having pixels from projection data;
A discrete total variation (TV) minimization unit for setting a set of predetermined values indicating an increase or decrease in the gradient direction of the total variation in a given pixel, the total for each of the previous SL pixels determining the discrete gradient of variation, the discrete gradient indicates low down the increase or the, each pixel value before Symbol pixel, the direction index towards Te the gradient direction odor with respect to the one pixel in the pixel An X-ray computer comprising: a discrete total variation (TV) minimizing unit that, if equal to the discrete slope, changes by a predetermined value to reduce the total variation and repeats until a predetermined condition is reached Tomography equipment. A method for removing noise in an image,
initializing a direction index associated with each pixel of a) the image, the direction index indicates a small increase or decrease on Discrete gradient of total variation,
b) wherein for each pixel, determining a discrete gradient of the total variation, the discrete gradient shows a low decrease the increase or the,
c ) if the directional index and the discrete gradient are equal, changing the pixel value of each pixel by a predetermined value to reduce the total variation;
d ) repeating the steps from b) to c ) until a predetermined condition is reached. An image processing method for removing image noise,
i) a step of determining a discrete slope of total variation for each pixel, the discrete gradient shows a small increase or decrease, a step,
ii) changing each pixel value of the pixel by a predetermined value according to the discrete gradient;
and iii) repeating the step i) and the step ii) until a predetermined condition is reached. An image processing apparatus for removing noise in an image,
i) a means for determining a discrete slope of total variation for each pixel, the discrete gradient shows a small increase or decrease, and said means for determining,
ii) means for changing each pixel value of the pixel by a predetermined value according to the discrete gradient;
iii) an image processing apparatus comprising: means for repeatedly executing the means i) and the means ii) until a predetermined condition is reached.